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The problem you provided involves the analysis of simple harmonic motion (SHM) based on the velocity vs. time graph of an object.

### 1. Maximum Speed of the Object
The graph shows the velocity function of an object in SHM. From the graph, the **maximum speed** (absolute value of velocity) is clearly labeled as **1.2 m/s**, which is the amplitude of the velocity graph.

### 2. Times of Maximum Displacement
In SHM, maximum displacement occurs when the velocity is zero. From the graph, these times occur at the points where the graph crosses the horizontal axis (i.e., where \( v = 0 \)). Looking closely:

- The first zero crossing occurs around **0.15 s**.
- The second zero crossing occurs around **0.45 s**.

Both of these times are already correctly identified in the problem.

### 3. Maximum Displacement of the Object
The velocity function for SHM is given by:

\[
v(t) = -A \omega \sin(\omega t)
\]

where:
- \( A \) is the amplitude of displacement,
- \( \omega \) is the angular frequency.

The maximum speed is related to the maximum displacement by the equation:

\[
v_{\text{max}} = A \omega
\]

From the graph:
- Maximum speed \( v_{\text{max}} = 1.2 \, \text{m/s} \).

Now, let's determine the angular frequency \( \omega \). The period \( T \) is the time for one complete cycle. From the graph, the object completes one cycle from 0 to 0.6 seconds, so:

\[
T = 0.6 \, \text{seconds}
\]

The angular frequency is related to the period by:

\[
\omega = \frac{2\pi}{T} = \frac{2\pi}{0.6} \approx 10.47 \, \text{rad/s}
\]

Now, we can find the maximum displacement \( A \) using:

\[
1.2 = A \times 10.47 \quad \Rightarrow \quad A \approx \frac{1.2}{10.47} \approx 0.1147 \, \text{m}
\]

Thus, the **maximum displacement** of the object is approximately **0.115 meters**.

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### Relative Questions:
1. What is the relationship between velocity and displacement in SHM?
2. How do you derive the angular frequency from the period?
3. What is the significance of zero velocity in terms of displacement in SHM?
4. How can we use the maximum speed to calculate other properties of SHM, like energy?
5. What is the physical meaning of amplitude in the context of SHM?

**Tip:** In simple harmonic motion, the maximum displacement occurs when the velocity is zero, and the maximum speed occurs when the object passes through the equilibrium position.

The graph above shows the velocity of an object in simple harmonic motion as a function of time. What is the maximum speed of the object? What are the first two times after zero at which the object has its maximum magnitude displacement from equilibrium? What is the maximum displacement of the object?

Analyze the velocity vs. time graph of an object in simple harmonic motion (SHM) to determine the maximum speed, times of maximum displacement, and the object's maximum displacement using key SHM formulas. Suitable for high school students studying SHM.

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